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Research Papers: Design Automation

Skeleton-Section Template Parameterization for Shape Optimization

[+] Author and Article Information
Ping Hu

Professor
School of Automotive Engineering,
Dalian University of Technology,
Dalian 116024, Liaoning, China
e-mail: pinghu@dlut.edu.cn

Lei Yang

School of Automotive Engineering,
Dalian University of Technology,
Dalian 116024, Liaoning, China
e-mail: lyangdut@mail.dlut.edu.cn

Baojun Li

School of Automotive Engineering,
Dalian University of Technology,
Dalian 116024, Liaoning, China
e-mail: bjli@dlut.edu.cn

Contributed by the Design Automation Committee of ASME for publication in the JOURNAL OF MECHANICAL DESIGN. Manuscript received January 9, 2018; final manuscript received May 31, 2018; published online September 18, 2018. Assoc. Editor: Nam H. Kim.

J. Mech. Des 140(12), 121404 (Sep 18, 2018) (10 pages) Paper No: MD-18-1024; doi: 10.1115/1.4040487 History: Received January 09, 2018; Revised May 31, 2018

A technique based on a skeleton-section template for parameterizing finite element (FE) models is reported and applied to shape optimization of thin-walled beam components. The template consists of a skeletal curve and a set of cross-sectional profiles. The skeletal curve can be used to derive global model variations, while the cross section is designed to obtain local deformations of the given shape. A mesh deformation method based on the radial basis functions (RBF) interpolation is employed to derive the shape variations. Specifically, the skeleton-embedding space and an anisotropic distance metric are introduced to improve the RBF deformation method. To validate the applicability of the proposed template-based parameterization technique to general shape optimization frameworks, two proof-of-concept numerical studies pertaining to crashworthiness design of an S-shaped frame were implemented. The first case study focused on global deformations with the skeletal curve, and the second treated the cross-sectional profiles as design parameters to derive local reinforcements on the model. Both studies showed the efficiency of the proposed method in generation of quality shape variants for optimization. From the numerical results, considerable amount of improvements in crashworthiness performances of the S-shaped frame were observed as measured by the peak crushing force (PCF) and the energy absorption. We conclude that the proposed template-based parameterization technique is suitable for shape optimization tasks.

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Figures

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Fig. 1

A mesh model of an S-shaped frame (upper) parameterized using the skeleton-section template (bottom)

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Fig. 2

Overview of the proposed framework for generating global or local shape variants based on the skeleton-section template parameterization and using the RBF-based deformation method

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Fig. 5

Displacement fields of a 2D example obtained using different distance metrics. Points with X = 0 and X = 10 are used as deformation handles, and their displacements can be seen from the bottom row: (a) diag(1, 1, 1), (b) diag(0.8, 1, 1), and (c) diag(0.2, 1, 1).

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Fig. 4

A shape variant (a) in Case 2 and the design variables and their feasible region (b). DV3 and DV4 are design variables shared by cross section 2 and 3, and DV5 and DV6 by cross section 6 and 7.

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Fig. 6

Mesh model embedded in the skeleton-conforming embedding space for geometric processing

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Fig. 7

Local deformation of a front rail mesh model extracted from a real-world automobile body structure. Modifications of cross-sections 2 and 3 are shown at the top row with cross-sections 1 and 4 fixed. Results using different metrics and obtained in different space are compared: (a) anistropic distance metric + skeleton-embedding space, (b) Euclidean distance metric + skeleton-embedding space, and (c) Euclidean distance metric + original space.

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Fig. 3

A shape variant and the design variables of the skeletal curve in case 1. The skeletal curve is a cubic Bézier curve and its second and third control points can be shifted along the X-axis. At the bottom row, the original skeletal curve along withits rotational minimizing frames are compared with the deformed curve and its frames.

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Fig. 8

Boundary and loading conditions of the S-shaped frame

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Fig. 9

Pareto offsprings, top 10 offsprings, and sample and their mean responses in both case studies plotted in terms of the crashworthiness performances (phenotypes) and of the design variables (genotypes): (a) case 1: phenotypes and genotypes and (b) case 2: phenotypes and genotypes

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Fig. 11

Crushing sequences of the baseline model and representative models of cases 1 and 2

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Fig. 10

Curves of internal energies and crushing forces of different models against time. C1Opt and C2Opt denote the representative models of cases 1 and 2, respectively.

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Fig. 12

The proposed template parameterization integrated into general optimization frameworks

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